211 research outputs found
Control of coupled oscillator networks with application to microgrid technologies
The control of complex systems and network-coupled dynamical systems is a
topic of vital theoretical importance in mathematics and physics with a wide
range of applications in engineering and various other sciences. Motivated by
recent research into smart grid technologies we study here control of
synchronization and consider the important case of networks of coupled phase
oscillators with nonlinear interactions--a paradigmatic example that has guided
our understanding of self-organization for decades. We develop a method for
control based on identifying and stabilizing problematic oscillators, resulting
in a stable spectrum of eigenvalues, and in turn a linearly stable synchronized
state. Interestingly, the amount of control, i.e., number of oscillators,
required to stabilize the network is primarily dictated by the coupling
strength, dynamical heterogeneity, and mean degree of the network, and depends
little on the structural heterogeneity of the network itself
Collective frequency variation in network synchronization and reverse PageRank
A wide range of natural and engineered phenomena rely on large networks of
interacting units to reach a dynamical consensus state where the system
collectively operates. Here we study the dynamics of self-organizing systems
and show that for generic directed networks the collective frequency of the
ensemble is {\it not} the same as the mean of the individuals' natural
frequencies. Specifically, we show that the collective frequency equals a
weighted average of the natural frequencies, where the weights are given by an
out-flow centrality measure that is equivalent to a reverse PageRank
centrality. Our findings uncover an intricate dependence of the collective
frequency on both the structural directedness and dynamical heterogeneity of
the network, and also reveal an unexplored connection between synchronization
and PageRank, which opens the possibility of applying PageRank optimization to
synchronization. Finally, we demonstrate the presence of collective frequency
variation in real-world networks by considering the UK and Scandinavian power
grids
Erosion of synchronization in networks of coupled oscillators
We report erosion of synchronization in networks of coupled phase
oscillators, a phenomenon where perfect phase synchronization is unattainable
in steady-state, even in the limit of infinite coupling. An analysis reveals
that the total erosion is separable into the product of terms characterizing
coupling frustration and structural heterogeneity, both of which amplify
erosion. The latter, however, can differ significantly from degree
heterogeneity. Finally, we show that erosion is marked by the reorganization of
oscillators according to their node degrees rather than their natural
frequencies.Comment: 5 pages, 4 figure
Higher order interactions in complex networks of phase oscillators promote abrupt synchronization switching
© 2020, The Author(s). Synchronization processes play critical roles in the functionality of a wide range of both natural and man-made systems. Recent work in physics and neuroscience highlights the importance of higher-order interactions between dynamical units, i.e., three- and four-way interactions in addition to pairwise interactions, and their role in shaping collective behavior. Here we show that higher-order interactions between coupled phase oscillators, encoded microscopically in a simplicial complex, give rise to added nonlinearity in the macroscopic system dynamics that induces abrupt synchronization transitions via hysteresis and bistability of synchronized and incoherent states. Moreover, these higher-order interactions can stabilize strongly synchronized states even when the pairwise coupling is repulsive. These findings reveal a self-organized phenomenon that may be responsible for the rapid switching to synchronization in many biological and other systems that exhibit synchronization without the need of particular correlation mechanisms between the oscillators and the topological structure
Memory selection and information switching in oscillator networks with higher-order interactions
We study the dynamics of coupled oscillator networks with higher-order
interactions and their ability to store information. In particular, the fixed
points of these oscillator systems consist of two clusters of oscillators that
become entrained at opposite phases, mapping easily to information more
commonly represented by sequences of 0's and 1's. While such fixed point
states exist in a system of oscillators, we find that a relatively small
fraction of these are stable, as chosen by the network topology. To understand
the memory selection of such oscillator networks, we derive a stability
criterion to identify precisely which states are stable, i.e., which pieces of
information are supported by the network. We also investigate the process by
which the system can switch between different stable states when a random
perturbation is applied that may force the system into the basin of attraction
of another stable state
Memory selection and information switching in oscillator networks with higher-order interactions
We study the dynamics of coupled oscillator networks with higher-order interactions and their ability to store information. In particular, the fixed points of these oscillator systems consist of two clusters of oscillators that become entrained at opposite phases, mapping easily to information more commonly represented by sequences of 0’s and 1’s. While 2 such fixed point states exist in a l system of N oscillators, we find that a relatively small fraction of these are stable, as chosen by the network topology. To understand the memory selection of such oscillator networks, we derive a stability criterion to identify precisely which states are stable, i.e., which pieces of information are supported by the network. We also investigate the process by which the system can switch between different stable states when a random perturbation is applied that may force the system into the basin of attraction of another stable state.
Applying CAD/CAE/CAM Techniques for Optimizing the Design and Reducing the Cost of a Pediatric Stander
A pediatric stander is an adapted piece of equipment whose function is to achieve the vertical position of the child when motor control is inadequate, in other words, when the child cannot stand and control his weight against gravity, having the age to do it. This technical equipment is necessary for patients diagnosed with cerebral palsy who have already acquired head control and initiated trunk control. This product has a high value in Peru. For the generation of this equipment, we will apply a computer editing and design process, we will follow a 5-step process in addition to applying CAD, CAE, and CAM techniques, emphasizing the design optimization method. Finally, we will verify how the application of this methodology, together with computer simulation, allows us to generate a functional, resistant prototype and, in the main point, with optimization in design and acquisition costs
- …